References
- Y. Mi, M. A. Crisfield, G. A. O. Davies, and H. B. Hellweg, “Progressive delamination using interface elements,” J. Composite Mater., vol. 32, no. 14, pp. 1246–1272, 1998. DOI: https://doi.org/10.1177/002199839803201401.
- J. C. J. Schellekens and R. De Borst, “A non-linear finite element approach for the analysis of mode-I free edge delamination in composites,” Int. J. Solids Struct., vol. 30, no. 9, pp. 1239–1253, 1993. DOI: https://doi.org/10.1016/0020-7683(93)90014-X.
- A. Turon, C. G. Davila, P. P. Camanho, and J. Costa, “An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models,” Eng. Fracture Mech., vol. 74, no. 10, pp. 1665– 1682, 2007. DOI: https://doi.org/10.1016/j.engfracmech.2006.08.025.
- S. Jiménez and R. Duddu, “On the parametric sensitivity of cohesive zone models for high-cycle fatigue delamination of composites,” Int. J. Solids Struct., vol. 82, pp. 111–124, 2016. DOI: https://doi.org/10.1016/j.ijsolstr.2015.10.015.
- G. Ghosh, R. Duddu and C. Annavarapu, “A stabilized finite element method for enforcing stiff anisotropic cohesive laws using interface elements,” Computer Methods Appl. Mech. Eng., vol. 348, pp. 1013–1038, 2019. DOI: https://doi.org/10.1016/j.cma.2019.02.007.
- G. Alfano and M. A. Crisfield, “Finite element interface models for the delamination analysis of laminated composites: Mechanical and computational issues,” Int. J. Numer. Meth. Engng., vol. 50, no. 7, pp. 1701–1736, 2001. DOI: https://doi.org/10.1002/nme.93.
- P. P. Camanho, C. G. Davila, and M. F. De Moura, “Numerical simulation of mixed-mode progressive delamination in composite materials,” J. Compos. Mater., vol. 37, no. 16, pp. 1415–1438, 2003. DOI: https://doi.org/10.1177/0021998303034505.
- W. G. Jiang, S. R. Hallett, B. G. Green, and M. R. Wisnom, “A concise interface constitutive law for analysis of delamination and splitting in composite materials and its application to scaled notched tensile specimens,” Int. J. Numer. Meth. Engng, vol. 69, no. 9, pp. 1982–1995, 2007. DOI: https://doi.org/10.1002/nme.1842.
- A. Turon, P. P. Camanho, J. Costa, and J. Renart, “Accurate simulation of delamination growth under mixed-mode loading using cohesive elements: Definition of interlaminar strengths and elastic stiffness,” Compos. Struct., vol. 92, no. 8, pp. 1857–1864, 2010. DOI: https://doi.org/10.1016/j.compstruct.2010.01.012.
- W. Zhang, A. Tabiei and D. French, “Comparison between discontinuous galerkin method and cohesive element method: On the convergence and dynamic wave propagation issue,” Int. J. Comput. Methods Engng. Sci. Mech., vol. 19, no. 5, pp. 363–373, 2018. DOI: https://doi.org/10.1080/15502287.2018.1535527.
- X. Lu, M. Ridha, B. Y. Chen, V. B. C. Tan, and T. E. Tay, “On cohesive element parameters and delamination modelling,” Engineering Fracture Mech., vol. 206, pp. 278– 296, 2019. DOI: https://doi.org/10.1016/j.engfracmech.2018.12.009.
- Y. Freed and L. Banks-Sills, “A new cohesive zone model for mixed mode interface fracture in bimaterials,” Engng. Fracture Mech., vol. 75, no. 15, pp. 4583–4593, 2008. DOI: https://doi.org/10.1016/j.engfracmech.2008.04.013.
- P. W. Harper and S. R. Hallet, “Cohesive zone length in numerical simulations of composite delamination,” Engng. Fracture Mech., vol. 75, no. 16, pp. 4774–4792, 2008. DOI: https://doi.org/10.1016/j.engfracmech.2008.06.004.
- J. C. J. Schellekens and R. De Borst, “On the numerical integration of interface elements,” Int. J. Numer. Meth. Engng., vol. 36, no. 1, pp. 43–66, 1993. DOI: https://doi.org/10.1002/nme.1620360104.
- M. G. G. V. Elices, G. V. Guinea, J. Gomez, and J. Planas, “The cohesive zone model: Advantages, limitations and challenges,” Engng. Fracture Mech., vol. 69, no. 2, pp. 137–163, 2002. DOI: https://doi.org/10.1016/S0013-7944(01)00083-2.
- R. D. Borst, “Numerical aspects of cohesive-zone models,” Engng. Fracture Mech., vol. 70, no. 14, pp. 1743–1757, 2003. DOI: https://doi.org/10.1016/S0013-7944(03)00122-X.
- A. Simone, “Partition of unity-based discontinuous elements for interface phenomena: Computational issues,” Int. J. Numer. Methods Biomed. Engng., vol. 20, no. 6, pp. 465–478, 2004.
- Q. Yang and B. Cox, “Cohesive models for damage evolution in laminated composites,” Int. J. Fract., vol. 133, no. 2, pp. 107–137, 2005. DOI: https://doi.org/10.1007/s10704-005-4729-6.
- T. Q. Thai, T. Rabczuk, and X. Zhuang, “Numerical study for cohesive zone model in delamination analysis based on higher-order B-spline functions,” J. Micromech. Mol. Phys., vol. 2, no. 1, pp. 1750004, 2017. DOI: https://doi.org/10.1142/S2424913017500047.
- K. Park, G. H. Paulino, and J. R. Roesler, “A unified potential-based cohesive model of mixed-mode fracture,” J. Mech. Phys. Solids, vol. 57, no. 6, pp. 891–908, 2009. DOI: https://doi.org/10.1016/j.jmps.2008.10.003.
- C. G. Dávila, P. P. Camanho, and A. Turon, “Effective simulation of delamination in aeronautical structures using shells and cohesive elements,” J. Aircraft, vol. 45, no. 2, pp. 663–672, 2008. DOI: https://doi.org/10.2514/1.32832.
- C. G. Dávila, C. A. Rose, and P. P. Camanho, “A procedure for superposing linear cohesive laws to represent multiple damage mechanisms in the fracture of composites,” Int. J. Fract., vol. 158, no. 2, pp. 211–223, 2009. DOI: https://doi.org/10.1007/s10704-009-9366-z.
- Q. D. Yang, X. J. Fang, J. X. Shi, and J. Lua, “An improved cohesive element for shell delamination analyses,” Int. J. Numer. Meth. Engng., vol. 83, no. 5, pp. 611–641, 2010. DOI: https://doi.org/10.1002/nme.2848.
- B. C. Do, W. Liu, Q. D. Yang, and X. Y. Su, “Improved cohesive stress integration schemes for cohesive zone elements,” Engng. Fracture Mech., vol. 107, pp. 14–28, 2013. DOI: https://doi.org/10.1016/j.engfracmech.2013.04.009.
- W. Cui and M. R. Wisnom, “A combined stress-based and fracture-mechanics-based model for predicting delamination in composites,” Composites, vol. 24, no. 6, pp. 467–474, 1993. DOI: https://doi.org/10.1016/0010-4361(93)90016-2.
- D. Xie and A. M. Waas, “Discrete cohesive zone model for mixed-mode fracture using finite element analysis,” Engng. Fracture Mech., vol. 73, no. 13, pp. 1783–1796, 2006. DOI: https://doi.org/10.1016/j.engfracmech.2006.03.006.
- X. Liu, R. Duddu, and H. Waisman, “Discrete damage zone model for fracture initiation and propagation,” Engng. Fracture Mech., vol. 92, pp. 1–18, 2012. DOI: https://doi.org/10.1016/j.engfracmech.2012.04.019.
- Y. Wang and H. Waisman, “Progressive delamination analysis of composite materials using XFEM and a discrete damage zone model,” Comput Mech., vol. 55, no. 1, pp. 1–26, 2015. DOI: https://doi.org/10.1007/s00466-014-1079-0.
- E. Svenning, “A weak penalty formulation remedying traction oscillations in interface elements,” Computer Methods Appl. Mech. Engng., vol. 310, pp. 460–474, 2016. DOI: https://doi.org/10.1016/j.cma.2016.07.031.
- P. Hansbo, “Nitsche’s method for interface problems in computational mechanics,” GAMM-Mitteilungen, vol. 28, no. 2, pp. 183–206, 2005. DOI: https://doi.org/10.1002/gamm.201490018.
- V. P. Nguyen, “Discontinuous Galerkin/extrinsic cohesive zone modeling: Implementation caveats and applications in computational fracture mechanics,” Engng. Fracture Mech., vol. 128, pp. 37–68, 2014. DOI: https://doi.org/10.1016/j.engfracmech.2014.07.003.
- M. Juntunen and R. Stenberg, “Nitsche’s method for general boundary conditions,” Math. Comp., vol. 78, no. 267, pp. 1353–1374, 2009. DOI: https://doi.org/10.1090/S0025-5718-08-02183-2.
- Abaqus Analysis User’s Guide, Version 6.14 , Providence, RI: Dassault Systemes Simulia Corp., 2014.
- C. Annavarapu, M. Hautefeuille, and J. E. Dolbow, “Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods,” Int. J. Numer. Meth. Engng., vol. 92, no. 2, pp. 206–228, 2012. DOI: https://doi.org/10.1002/nme.4343.
- D. N. Arnold, F. Brezzi, B. Cockburn and L. D. Marini, “Unified analysis of discontinuous Galerkin methods for elliptic problems,” SIAM J. Numer. Anal., vol. 39, no. 5, pp. 1749–1779, 2002. DOI: https://doi.org/10.1137/S0036142901384162.
- R. Liu, M. F. Wheeler, and C. N. Dawson, “A three-dimensional nodal-based implementation of a family of discontinuous Galerkin methods for elasticity problems,” Computers Struct., vol. 87, no. 3–4, pp. 141–150, 2009. DOI: https://doi.org/10.1016/j.compstruc.2008.11.009.
- C. Annavarapu, M. Hautefeuille, and J. E. Dolbow, “A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: Single interface,” Computer Methods Appl. Mech. Engng., vol. 268, pp. 417–436, 2014. DOI: https://doi.org/10.1016/j.cma.2013.09.002.
- C. Annavarapu, M. Hautefeuille, and J. E. Dolbow, “A robust Nitsche’s formulation for interface problems,” Computer Methods Appl. Mech. Engng., vol. 225–228, pp. 44–54, 2012. DOI: https://doi.org/10.1016/j.cma.2012.03.008.
- J. D. Sanders, T. A. Laursen and M. A. Puso, “A Nitsche embedded mesh method,” Comput Mech., vol. 49, no. 2, pp. 243–257, 2012. DOI: https://doi.org/10.1007/s00466-011-0641-2.
- A. Embar, J. Dolbow, and I. Harari, “Imposing Dirichlet boundary conditions with Nitsche’s method and spline-based finite elements,” Int. J. Numer. Meth. Engng., vol. 83, no. 7, pp. 877–898, 2010. DOI: https://doi.org/10.1002/nme.2863.
- D. Versino, H. M. Mourad, C. G. Davila, and F. L. Addessio, “A thermodynamically consistent discontinuous Galerkin formulation for interface separation,” Compos. Struct., vol. 133, pp. 595–606, 2015. DOI: https://doi.org/10.1016/j.compstruct.2015.07.080.
- S. Jiménez, X. Liu, R. Duddu, and H. Waisman, “A discrete damage zone model for mixed-mode delamination of composites under high-cycle fatigue,” Int. J. Fract., vol. 190, no. 1–2, pp. 53–74, 2014. DOI: https://doi.org/10.1007/s10704-014-9974-0.
- J. N. Reddy and A. Miravete, Practical Analysis of Composite Laminates. Boca Raton, FL: CRC press, 2018.
- E. A. Armanios, R. B. Bucinell, D. W. Wilson, L. E. Asp, A. SjöGren, and E. S. Greenhalgh, “Delamination growth and thresholds in a carbon/epoxy composites under fatigue loading,” J. Compos. Technol. Res., vol. 23, no. 2, pp. 55–68, 2001. DOI: https://doi.org/10.1520/CTR10914J.
- S. H. Song, G. H. Paulino, and W. G. Buttlar, “A bilinear cohesive zone model tailored for fracture of asphalt concrete considering viscoelastic bulk material,” Engng. Fracture Mech., vol. 73, no. 18, pp. 2829–2848, 2006. DOI: https://doi.org/10.1016/j.engfracmech.2006.04.030.
- S. R. Hallett, B. G. Green, W. G. Jiang, and M. R. Wisnom, “An experimental and numerical investigation into the damage mechanisms in notched composites,” Compos. Part A: Appl. Sci. Manufacturing, vol. 40, no. 5, pp. 613–624, 2009. DOI: https://doi.org/10.1016/j.compositesa.2009.02.021.